Modeling and Prediction

8/3/2019 Modeling and Prediction

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Proceedings of the Fortieth Turbomachinery Symposium

September 12-15, 2011, Houston, Texas

MODELING AND PREDICTION OF SIDESTREAM INLET PRESSURE FOR MULTISTAGE CENTRIFUGAL

COMPRESSORS

Jay Koch

Principal Engineer

Dresser-Rand

Olean, NY, USA

Jim Sorokes

Principal Engineer

Dresser-Rand

Olean, NY, USA

Moulay Belhassan

Principal Engineer

Dresser-Rand

Olean, NY, USA

.

ABSTRACT

It is common for some compressors in certain applications

to have one or more incoming sidestreams that introduce flow

other than at the main inlet to mix with the core flow. In most

cases, the pressure levels at these sidestreams must be

accurately predicted to meet contractual performance

guarantees. The focus of this paper is the prediction of

sidestream flange pressure when the return channel outlet

conditions are provided. A model to predict the impact of local

curvature in the mixing section is presented and compared with

both Computational Fluid Dynamics work and measured test

data.

INTRODUCTION

Despite recent advances in analytical tools, developers and

users of state-of-the-art centrifugal compressor equipment

continue to rely heavily on testing to ultimately confirm the

performance of new components or stages. This is especially

true in heavy hydrocarbon applications such as compressors

used in liquefied natural gas (LNG), ethylene, or gas-to-liquid

facilities. Heavy hydrocarbon gases have very low gas sonic

velocities that produce high Mach numbers in the aerodynamic

flowpath. By their nature, such high Mach number, high flow

coefficient stages have very narrow flow maps characterized by

limited choke and surge margin. In addition, many of theseapplications require the machines with sidestreams (or

sideloads) to accommodate the flows entering and/or exiting

the compressor as determined by the particular process for

which they are intended. The sidestreams and associated

mixing further complicate the performance prediction process

because the pressure, temperature and flow conditions at each

one of these sidestreams as well as at the exit of the machine

must be met within stringent tolerances to optimize the amount

of end product delivered by the process. Therefore, it is

imperative that the compressor OEM and end user have a firm

grasp of the performance characteristics of any impellers

diffusers, return channels, and/or other flow path components

used in such equipment.

The high cost associated with delays in the projec

schedule increase the attractiveness of design and testing

methods that ensure these machines meet the contractua

operating requirements the first time; without the need for

repeated modifications and test iterations to correc

performance shortfalls. Given the size, construction style, and

in-house test piping arrangements for many large centrifugals

one modification / re-test iteration could take several weeks

Repeated iterations on the OEMs test facility could delay the

start-up of a new plant by months, leading to lost production /

revenue for the end user as well as lost revenue and reputationfor the compressor OEM. Consequently, OEMs spend

continually work to enhance their performance prediction

methods. This paper details work done toward that end.

This paper is the latest in a continuing series of publications

describing work completed in association with a novel test

vehicle that was designed to replicate the performance of a full-

scale, large frame-size, multi-stage centrifugal compressor for

high flow coefficient, high Mach number stages. The test

vehicle, described by Sorokes et al (2009), is equipped with a

vast array of internal instrumentation that make it possible to

evaluate the aero/thermodynamic and mechanical behavior of a

compressor. Sufficient instrumentation is installed to allow

assessment of the entire compressor as well as individualcomponents or combinations of components. Of particular

interest to this study, the test rig included instrumentation at

critical locations within the sidestream components to permit an

assessment of the losses through each sidestream element.

BACKGROUND

As part of the compressor selection and design process, the

OEM must be able to predict the performance of the overall

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unit from inlet to discharge flange. For a simple, so-called

straight through compressor, this means predicting the

performance for each stage (inlet guide / impeller / diffuser /

return channel or volute) in series from the inlet to the

discharge of the machine. However, for units with one or more

incoming sidestreams, there is the additional task of accounting

for the impact of the sidestream and thereby predicting the

conditions at the intermediate flange; i.e., static and total

pressure.

Typically, OEMs supply compressor performance curves

that reflect flange-to-flange performance because that is what

the process engineer needs to ensure proper operation of their

system. Such data is easier to monitor when a compressor is

installed in the field. However, flange-to-flange data, if not

interpreted properly can lead to misleading conclusions as to

the relative performance of individual sections of a

compression system. For example, if the sidestream losses

from the flange to mixing section are attributed to the upstream

section, it will cause the upstream section to appear low in

performance while the downstream section will show

erroneously high performance levels; i.e., efficiency

significantly higher than 90%). The need for a more refined

method for allocating sidestream losses as well as the need to

eliminate other uncertainties regarding the sidestream lossmechanisms has led to additional research on sidestream

performance modeling.

Compressor OEMs have completed significant work in

recent years to improve their understanding of the flow in

sidestreams and sidestream mixing section as well as the impact

of the mixed stream on the downstream impeller. In most

cases, the portion of the sidestream from the flange connection

to the mixing section (i.e., the location where the incoming

sidestream flow mixes with the core flow) is very similar to a

radial compressor inlet. There has been significant work

reported in the literature on radial inlets. For example, Flathers

et al (1994) compared several geometric variations using

Computational Fluid Dynamics (CFD) and measured testresults. Koch et al (1995), Kim and Koch (2004), Michelass

and Giachi (1997) subsequently reported similar work on

different geometric variations. These studies all led to

increased understanding of the flow structure and improved

prediction methods for inlet losses and the details of the flow

field exiting these components. Proper use of the CFD tools

also led to more efficient / effective inlet configurations that

provided a more circumferentially uniform flow to the

downstream impeller. The studies also aided in the one-

dimensional prediction of pressure losses.

Additional studies, which included the upstream return

channel and the complete sidestream geometry, have been

completed to accurately model the flow where the core flow

and sidestream flow merge. While this location is typically

called the mixing section as noted above, the flows do not

completely mix before entering the impeller. The works of

Sorokes et al (2000 and 2006) and the prior referenced work on

radial inlets have led to a greater comprehension of the

complex flows at the sidestream mixing location. However,

these works did not address the flow physics that determine the

static pressure in the mixing section, which, in turn, sets the

flange pressure level. The study by Hardin (2002) describes a

one-dimensional method that determines how the flow at the

mixing location and, therefore, the local static pressure is

impacted by the local flow curvature.

This paper presents predictions for two geometric

configurations that violate the assumptions made in previous

studies, resulting in a need to modify the relevant equations

Additionally, the prior work did not present the methods used to

predict the total pressure downstream of the mixing section

This paper will present various methods to predict the

downstream total pressure and compare the analytical results to

measured test data on the two geometries.

INVESTIGATIVE STUDY

As part of a recent OEM development program, a study on

several sidestream configurations was conducted. The projec

required compact sidestream mixing sections; i.e., mixing

sections that take less axial length; in a compressor with high

flow coefficient ( > 0.10) and high machine Mach number

(i.e., U2/A0 > 1.1). The sidestreams were of different sizes a

the incoming flows represented different percentages of the

flow from the upstream section. The gas density in the

sidestreams also varied due to the increasing pressure in the

machine. Finally, the machine was tested using a high mole

weight refrigerant to replicate the high gas densities and Machnumbers. Representative geometry for a typical configuration

is shown in Figures 1a and 1b.

Figure1a. Geometry for configuration 1

Figure1b. Geometry for configuration 1 section A- A

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During the detailed design process, each proposed stage

geometry was modeled using a commercially available CFD

code, ANSYS CFX-10. As part of this study, the sidestream

inlet geometry was optimized within the available axial space

provided. The CFD domain for each sidestream included the

upstream diffuser, return channel, sidestream nozzle, sidestream

plenum, mixing section, and downstream impeller. The full

360-degree model included all passages to evaluate any

circumferential flow non-uniformity at the exit of the

sidestream. The upstream impeller was not included to reduce

the size of the computational domain, thereby reducing solution

time. This simplification also allowed the return channel exit

conditions to be varied for different flow conditions; i.e., to

replicate the flow conditions from maximum (choke) to

minimum stable flow (stall / surge). Because the objective of

the study was to predict the sidestream flange pressure, when

provided return channel exit conditions, it was felt this

simplification would have a minimal impact on the flow

physics of interest.

The geometry was modeled using a combination of

hexahedral and tetrahedral elements. All axisymmetric

components, such as the diffuser and return channel, were

modeled using hexahedral elements and the non-uniform

components, such as the sidestream nozzle and plenum section,were modeled using tetrahedral elements because such

components are more easily modeled using tets. The grids

were refined for each component and grid element type as it is

recognized that higher grid densities are required for tetrahedral

as opposed to hexahedral elements. Each component had a grid

size of approximately 2 million elements and the total grid size

was approximately 6 million elements. For the sidestream

inlet, the grid density used is similar to those reported by the

current authors in Kim and Koch (2004).

The boundary conditions of the model were based on the

one-dimensional predictions used to select and size the

hardware. The prescribed flow angle, total pressure and totaltemperature were specified at the diffuser entrance. Total

temperature and mass flow were specified at the sidestream

entrance and total mass flow was specified at the exit of the

computational domain. The inlet pressure at the sidestream

entrance was the objective function of the analysis.

A second order discretization scheme was used for the

simulation and standard k- model was adopted as a turbulence

model combined with a scalable wall function approach that

eliminates the necessity of discretely resolving the large

gradients in the thin, near-wall region. The convergence

criterion was set to the maximum residual of 10-4

for u, v, w,

and p.

For the two sidestream configurations addressed in thispaper, the internal elements, return channel vanes, sidestream

vanes and inlet guide vanes, were fixed during the optimization.

Only the meridional passage width was varied.

In the first configuration (designated Configuration 1), the

core flow (i.e., flow exiting the upstream return channel) and

incoming sidestreams flows were nearly equal. This geometry

is shown in Figures 1a and 1b. The second configuration

(Configuration 2) was for a higher pressure and hence higher

density stage and had a core flow that was much greater than

the sidestream flow. The details of this mixing section

geometry can be seen in Figure 2.

Figure 2. Mixing section geometry for configuration 2

The design values of area ratio (return channel exit area to

sidestream exit area), density, and return channel exit Mach

number are provided in Table 1.

Table 1. Sidestream Design Parameters

The results of the CFD study are shown in Figures 3-6

The Mach number distribution in the sidestream nozzle for

configuration 1 is shown in Figure 3. This configuration show

the vane rows in the sidestream are oriented with the flow to

provide a circumferentially uniform velocity profile at the exit

of the sidestream. A meridional view providing the Mach

number distribution in the mixing section is shown in Figure 4This plot shows a variation in the Mach number across the

sidestream exit. The variation in Mach number is also eviden

at the exit of the return channel as the flow turns to enter the

downstream impeller.

Density Area Ratio Mach

lb/ft3

Main/Sidestream Number

1 0.30 0.76 0.34

2 1.00 4.96 0.26

Configuration

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Figure 3. Mach number in sidestream configuration 1

Figure 4. Mach number at sidestream mixing location -

configuration 1

Figure 5. Static pressure at the sidestream mixing location -

configuration 1

Figure 6. Static pressure at the sidestream mixing location

configuration 2

Contours of the static pressure at the same location are

shown in Figure 5. It is evident from this figure that the static

pressure varies from the shroud wall at the exit of the

sidestream to the hub wall downstream of the return channel

Because of the lower static pressure at the sidestream exit, the

total pressure at this location is lower even though the velocity

upstream of the curvature is roughly matched for both streams.

This phenomenon of reduced pressure at the sidestream

exit was predicted by Hardin (2002). Based on the

relationships shown in that work, this variation in pressure can

be expected to increase with dynamic pressure, 22V , and

with larger variations in curvature between the two streams.

A plot of static pressure for configuration 2 is shown in

Figure 6. This configuration shows similar trends to

configuration 1 with significant variation in the static pressure

from the exit of the return channel to the exit of the sidestream.

In reviewing these configurations it is evident that the

specific formulation developed in the prior work does not apply

to this geometry. A major assumption put forth in the prior

work was that there was no variation in the static pressure at the

outlet of the return channel passage. Thus the effect o

curvature was only applied across the sidestream exit. For this

geometry, the formulation must be modified to account for the

variation across both the return channel exit and the sidestream

exit. While simple in nature, this can have a significant impac

on the predicted static pressure at the sidestream exit.

Before developing a method to account for the changes in

curvature, an optimization study was conducted on the mixing

section of configuration 2. To reduce the execution time and

allow for more design iterations, a sub-model was created that

included a portion of the return channel vane exit and a portion

of the exit of the plenum section of the sidestream just upstream

of the mixing section. The upstream diffuser and return

channel as well as the sidestream plenum were removed from

the sub-model. This also allowed the geometry to be modeled

as a pie slice section as opposed to a full 360 model

Comparison of sub-model and full model solutions revealedthat the simplified model captured the important flow features

in the mixing section. Therefore, the simplified model was

used for the optimization study for the mixing section.

PREDICTION METHODOLOGY

To accurately predict the sidestream exit conditions, proper

boundary conditions for the problem must be established. The

exit conditions at the return channel are generally known from

one-dimensional predictions or from test measurements

Therefore, for this discussion it was assumed the discharge tota

pressure was known at the exit of the return channel preceding

the mixing section. Additionally, it is assumed the area, flowrate, temperature and gas properties were known at the return

channel exit and at the sidestream exit.

Given the referenced information, the return channel exi

mean velocity and static pressure can be calculated. Based on

basic flow principles, it was assumed that the static pressure

was equal between both flow streams at the mixing location

The only location where this is true is at the shroud wall at the

exit of the return channel and the hub wall at the exit of the

sidestream. This assumption is supported by the previou

computational study completed by the OEM and by other

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researchers such as Hardin (2002). Unfortunately, the pressure

at this location is not as desired because of the local curvatures

in the mixing section. The desired result can be obtained via a

series of equations that allow the average static pressure at the

exit of the sidestream to be calculated from the average static

pressure at the exit of the return channel.

According to basic aerodynamic principles, the

relationship of pressure versus radius of curvature can be

expressed by Equation (1).

R

V

dR

dP2

= (1)

For the geometry shown in Figure 7, the average static

pressure at the exit of the return channel can be related to the

average pressure at the exit of the sidestream by the variation in

curvature using Equation 1. The average static pressure at the

sidestream exit is defined by Equation (2).

( )

t

sst

tss

c

cc

ss

R

RRVPP

Re

Re

Re

2

+=

(2)

Where:

sssP = Static pressure at sidestream exit

tsP

Re

= Static pressure at return channel exit

ssCR = Radius sidestream of curvature (see fig. 7)

tCR

Re

= Radius of return channel curvature (see fig. 7)

= Gas density

V = Velocity at the sidestream exit

Figure 7. Geometry for pressure prediction

Once the static pressure at the sidestream exit is

determined, the velocity and total pressure can be calculated.The flange total pressure can be calculated based on the

predicted losses in the nozzle plenum region, once the

sidestream exit total pressure is known (Equations (3) and (4)).

The losses in this region of the sidestream have been shown to

be consistent and predictable by 1-D models. The 1-D model

for a given geometry can be based on CFD prediction or based

on test measurements.

2

2V

PPssss sT

+= (3)

ss

FLG

TTLC

VPP

ssFLG 2

2

+= (4)

Where:

sssP = Static pressure at sidestream exit

ssTP = Total pressure at sidestream exit

FLGTP = Total pressure at flange

= Gas density

V = Velocity at sidestream exit

VFLG = Velocity at flange

LCss = Loss coefficient

The appropriate method for the prediction of the tota

pressure downstream of the mixing section at the inlet of the

impeller has not been questioned in the literature. The

appendix of the test standard from ASME (1997), defines a

momentum balance method, but this method is approximateAttempts to use this method have not been very successful for

these authors or others in the open literature. The impact of the

gradient in total pressure on the downstream impeller

performance varies greatly. Some CFD studies indicate a

significant impact on performance while other studies show a

minor impact. For 1-D performance prediction purposes a

single representative value of the impeller inlet pressure is

desired. This representative pressure should provide a

consistent reference between predicted performance and

measured test results. It is also desired that the selected value

provides a consistent reference for comparison between

performance prediction and measured test results.

When CFD results are evaluated, a mass-averaged totapressure at a selected plane is the common method for

evaluation. Evaluations of test results often use an arithmetic

average or area average based on total pressure measured by a

single pressure probe or multi-hole pressure rake. The prio

work by Hardin (2002) suggests mass-averaging the tota

pressure at the exit of each stream. To determine which method

provides a more consistent result, a set of evaluation criteria

was developed for use on future development tests. The tes

results will be evaluated using the three methods listed above to

determine which method provides a more consistent result and

therefore used for future comparisons between test results and

analytical predictions.

TEST DATA AND DISCUSSION

After completion of the design study, the OEM constructed

a full-scale development test rig; again, see Sorokes et al

(2009). As noted, the flow path of the test rig was heavily

instrumented to allow the measurement of the aero-

thermodynamic performance of the components of each stage

including the sidestream elements. The interna

instrumentation included total pressure probes, dynamic

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pressure probes, total temperature probes, and five-hole probes,

which measure both pressure and flow direction. A schematic

of the internal instrumentation layout used for each compressor

stage is given in Figure 8.

Figure 8. Test rig internal instrumentation layout

For each sidestream, the total pressure and temperature

were measured at the exit of the return channel and at the

sidestream exit. Additionally, the total pressure and

temperature distributions were measured near the exit of the

mixing section; i.e. just upstream of the impeller; via pressure

and temperature rakes. Therefore, it was possible to assess the

hub-to-shroud variation (or stratification) in pressure and

temperature due to the core / sidestream flow mixing.

In addition to the internal instrumentation, the total

pressure, total temperature and mass flow were measured at the

flange locations using standard combination pressure /

temperature probes.All performance testing was conducted using R-134A

refrigerant to achieve aerodynamic similitude at the design

conditions. The test measurements for each sidestream were

taken in accordance with the ASME PTC-10 test code from

ASME (1997).

To evaluate the revised prediction scheme, the predicted

sidestream exit total pressure was calculated at the test

conditions and compared with the measured total pressure on

test. The prediction was based purely on the known geometry

and test conditions.

For each sidestream configuration, data is presented for

different flow rates at a fixed impeller tip Mach number of

1.10. The flow ratio between the sidestream and the core flow

is maintained for all operating points using the OEM stringent

guidelines; i.e., more restrictive than the standard ASME Power

Test Code (see Kolata and Colby (1990)). The temperatures for

core flow and incoming sidestream streams were kept equal to

avoid heat transfer that would add uncertainty to the efficiency

calculation.

The results of the prediction for configuration 1 are shown

in Figure 9.

0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30

Return Channel Exit Mach Number

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

%ErrorinSidestreamExitTo

talPressure(Predicted/Measured)

Prediction with Curvature Correction

Prediction without Curvature Correction

Figure 9. Error between test and measurement with and withou

curvature correction configuration 1

The percent error in the sidestream exit predicted tota

pressure versus Mach number at the outlet of the return channe

is shown. For configuration 1 the prediction model is within

1.5% of the test results. As a means of determining the

suitability of this calculation, the percent error in sidestream

total pressure was also calculated without the curvature

correction. This comparison showed the sidestream exit tota

pressure was always over-predicted without the curvature

correction. For this application, failure to account for the

curvature effects resulted in an error of up to 5.8%. Simila

results for configuration 2 are shown in Figure 10.

0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28

Return Channel Exit Mach Number

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

%ErrorinSidestreamExitTotalPressure(Predicted/Measured)

Prediction with Curvature CorrectionPrediction without Curvature Correction

Figure 10. Error between test and measurement with and

without curvature correction configuration 2

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For configuration 2, the prediction model accounting for

curvature is also within 1.5% of the test results. The error

without the curvature correction is even greater than on

configuration 1, with a maximum difference of more than 6.1%.

Because there was considerable interest in the performance

of the sidestream and downstream impeller with off-design

flow functions, a set of conditions was defined to investigate

such operating conditions. These additional data provided

insight into prediction of the impeller inlet total pressure

downstream of a sidestream for off-design conditions.

During these tests the unit was intentionally tested at core

flow to sidestream flow ratios that were at the limits of the

ASME test standard (i.e., 10%), and thus considerably

different than the design values. Based on the curvature

prediction model, the flow function variation causes the

sidestream exit pressure (and thus flange pressure) to vary from

the design conditions. This would be true even if the

downstream impeller inlet conditions remain unchanged.

The change in flange pressure due to the different flow

ratios leads to variations in the calculated section performance

even though the impeller / diffuser / return channel

performance remains essentially unchanged. Recall that it was

possible to determine the performance from impeller exit to

return channel exit because of the additional instrumentationavailable in the test vehicle. The internal performance (based

on impeller inlet to return channel exit) and the flange to flange

performance are shown in Figure 11 for the same operating

conditions. There are small changes in the internal

performance for the various sidestream flow ratios, most likely

due to the impact on varying impeller inlet velocity profile due

to mixing effects at the off-design flow ratios. However,

there are more noticeable differences in the flange to flange

calculation, particularly toward the high capacity end of the

map.

0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15

Normalized Inlet Flow Coefficient

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

NormalizedHeadCoefficient

Flange-to-Flange -- Design Flow Ratio

Flange-to-Flange -- SS Flow > Design Flow Ratio

Internal -- Design Flow Ratio

Internal -- SS Flow > Design Flow Ratio

Figure 11. Flange to Flange and Internal Head Coefficient for

various sidestream flow ratios

As part of the prediction method discussion, data from

these tests were also used to evaluate which method of

determining the downstream impeller inlet condition provides

the best correlation with the test results. To complete thi

comparison, the impeller inlet condition was calculated three

ways. The first method was based on a mass-average of the

total pressures at the outlet of the return channel and the

sidestream exit. The second method used an arithmetic average

of the total pressure rake downstream of the mixing section

The third method was based on an area average of the

downstream rake pressures.

All three methods were compared using polytropic head

coefficient, p, versus inlet flow coefficient, , (see Figure 12).

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15

Normalized Inlet Flow Coefficient

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

NormalizedHeadCoefficient

Mass Avg - Design

Area Avg - Design

Arithmetic Avg - Design

Figure 12. Internal head coefficient for various total pressure

averaging methods at the mixing section

The data was normalized using the design point head and

flow coefficient and trends were reviewed for both design flow

and off-design flow conditions (i.e., from overload to

stall/surge). For each case, the basic impeller inlet similarity

condition remained the same. That is, the compressor was runat the same tip Mach number, and Reynolds number. However

the sidestream flow function was allowed to vary within the

limits of the ASME test code. As can be seen in the curves, the

different averaging methods did result in a change in the

perceived performance. This is not overly surprising because

the different averaging methods will result in a different inle

pressure to the downstream impeller and because the head

coefficient is directly dependent on the inlet pressure, the

resulting variation in head coefficient is to be expected.

Specifically, the change in inlet pressure due to the various

averaging techniques caused a shift in the inlet capacity and

also caused a change in the head coefficient as well as a change

in rise-to-surge for the area average method. The area-averagedmethod predicts a larger capacity and pressure coefficient than

either method. The mass-averaged result falls between the two

other methods. Based on this comparison, each method would

appear to provide a consistent basis for comparison with

predictions. The mass-averaged method has the advantage o

using a measured quantity that has less variation hub to shroud

than the other methods and is less sensitive to the flow ratio of

the core flow to the sidestream flow. Finally, the mass

averaging method also allows for a direct comparison between

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one-dimensional predictions, CFD and test results, as the

required information is typically readily available.

CONCLUSIONS

This paper presents results from a recent sidestream design

study and compares the analytical results to test measurements.

The new method builds on the prior works of Hardin (2002),

Sorokes et al (2000) and Sorokes et al (2006). Based on this

study, a modification to the published methodology has been

proposed to improve the calculation of the inlet pressure for

standard incoming sidestreams. Using the new method, it is

possible to predict the sidestream exit pressure within an

accuracy of 1.5%. This method enhancement will make it

possible to provide more accurate sidestream pressure levels,

thereby improving the process modeling for new or upgraded

facilities.

The comparison of test results with different averaging

methods has shown that each method offers consistent, though

somewhat different result. Based on this study, it is felt that

mass averaging of the core flow pressure and the sidestream

pressure provides the most effective reference for correlation of

the impeller inlet total pressure.

DISCLAIMER

The information contained in this document consists of

factual data, and technical interpretations and opinions which,

while believed to be accurate, are offered solely for

informational purposes. No representation or warranty is made

concerning the accuracy of such data, interpretations and

opinions.

NOMENCLATURE

V = VelocityR = Radius of Curvature

N = Rotational Speed

D = Impeller Outer Diameter

Q = Volume Flow

U = Tip Speed, DN

n = Polytropic Exponent,

2

1

1

2

ln

P

Pln

= Density

= Specific Volume

= Inlet Flow Coefficient,3

2 ND

Q

= Polytropic Head Coefficient,( )

2

1122

U

P-P1-n

n

PT = Total Pressure

PS = Static Pressure

TT = Total Temperature

Ret = Return Channel Exit

SS = Sidestream Exit

Flg = Sidestream Flange

REFERENCES

ASME, PTC 10, 1997, Performance Test Code on Compressors

and Exhausters, @ ASME Press.

Flathers, M., Bache, G., Rainsberger, R., 1994, An

Experimental and Computational Investigation of Flow in a

Radial Inlet of an Industrial Pipeline Centrifugal Compressor

@ ASME 94-GT-134.

Gilarranz, J., 2007, Actuation and Control of a Movable

Geometry System for a Large Frame-Size, Multi-Stage

Centrifugal Compressor Test Rig, @ ASME Paper GT2007-

27592, Submitted for Presentation at the GT2007, ASME Turbo

Expo 2007, Montreal, Canada.

Hardin, James R., 2002, A New Approach to Predicting

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ACKNOWLEDGEMENTS

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The authors thank Dresser-Rand Company for funding this

overall project and for allowing the publication of this work.

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